Abstract: A design of delay-dependent containment controller under the directed network graph is proposed in this study for a class of multi-agent system with time-varying communication delays. The proposed design can effectively drive all followers' states to asymptotically converge toward the convex hull spanned by the leaders. Combining Lyapunov stability theory and linear matrix inequality (LMI) method, a sufficient condition guaranteeing containment control is derived, and the problem of containment controller design is converted to solve the problem of ensuring the feasibility of linear matrix inequality. The results show that the delay-dependent containment controller effectively helps compensate the time-varying delays. Finally, the effectiveness and feasibility of the control method are verified by using a simulation example.